Uncertainty principle if position is restricted

[greypilgrim]

Hi.

Assume we have a large number of identical boxes of some finite length $l$ and with infinite potential walls. Let's prepare them all in the same momentum eigenstate. Since for eigenstates $\Delta p=0$, by the uncertainty principle $\Delta x$ should go to infinity. However, since the particles can't leave the boxes, $l$ is an upper limit for $\Delta x$. How is this possible?

 

[Orodruin]

There are no momentum eigenstates of the situation you are describing. They simply do not belong to the appropriate Hilbert space.

 

[greypilgrim]

Ok, but can we choose states such that $\Delta p$ is small enough (I guess not, that's probably why this doesn't work)?

 

[Demystifier]

Let's prepare them all in the same momentum eigenstate.

You cannot do that (if other conditions you mentioned are fulfilled).

 

[Demystifier]

Ok, but can we choose states such that $\Delta p$ is small enough (I guess not, that's probably why this doesn't work)?

Exactly!